Carbon dioxide dissolves in water to form carbonic acid, which is primarily dissolved CO2. Dissolved CO2 satisfies the equilibrium equation
CO2(g) <-> CO2(aq) K=0.032
The acid dissociation constants listed in most standard reference texts for carbonic acid actually apply to dissolved CO2. For a CO2 partial pressure of 1.9x10^-4 atm in the atmosphere, what is the pH of water in equilibrium with the atmosphere?
What I did:
K=[CO2(aq)]/[CO2(g)]
0.032 = [x]/(1.9x10^-4)
x = 6.08x10^-6
-log(6.08x10^-6) = 5.22 = pH
It says my answer is wrong, and this is the hint:
This is the negative logarithm of the [H2CO3]. Since H2CO3 is a weak acid, [H2CO3]=/=[H+]. Use the acid dissociation constant of H2CO3 to determine the [H+]. Then use the [H+] to calculate the pH.
Please help!
To solve this problem, you need to consider that the equilibrium equation you provided represents the reaction:
CO2(g) + H2O(l) <-> H2CO3(aq)
The equilibrium constant (K) of 0.032 represents the ratio of the concentration of dissolved CO2 ([CO2(aq)]) to the partial pressure of CO2 (PCO2) in the gas phase.
However, to determine the pH of water in equilibrium with the atmosphere, you need to consider the dissociation of carbonic acid (H2CO3) into H+ and HCO3- ions:
H2CO3(aq) <-> H+(aq) + HCO3-(aq)
The equilibrium constant for this dissociation reaction is the acid dissociation constant (Ka) of carbonic acid. The value of Ka for carbonic acid is typically provided in standard reference texts.
Here's how you can calculate the pH:
1. Calculate the concentration of H+ ions using the acid dissociation constant (Ka) and the concentration of H2CO3 ([H2CO3]) (which is equal to the concentration of dissolved CO2, [CO2(aq)]).
[H+] = sqrt(Ka * [H2CO3])
2. Calculate the pH using the concentration of H+ ions:
pH = -log[H+]
Now, let's apply this method to solve the problem.
Given:
PCO2 = 1.9x10^-4 atm
Ka (for carbonic acid) = provided in the standard reference text
1. Calculate the concentration of H2CO3 ([H2CO3]):
Using the equilibrium equation you provided:
K = [CO2(aq)] / [CO2(g)]
Given:
K = 0.032
[CO2(g)] = PCO2 = 1.9x10^-4 atm
[CO2(aq)] = K * [CO2(g)] = 0.032 * (1.9x10^-4) = 6.08x10^-6
Therefore, [H2CO3] = [CO2(aq)] = 6.08x10^-6
2. Calculate the concentration of H+ ions ([H+]):
Using the acid dissociation constant (Ka):
[H+] = sqrt(Ka * [H2CO3])
3. Calculate the pH:
pH = -log[H+]
Note: The value of Ka for carbonic acid should be provided in the problem or referred to in standard reference texts.
By following these steps, you should be able to calculate the pH of water in equilibrium with the atmosphere.